Commun Nonlinear Sci Numer Simulat 29 (2015) 170–178
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Commun Nonlinear Sci Numer Simulat
journal homepage: www.elsevier.com/locate/cnsns
Detection of noise effect on coupled neuronal circuits
Guodong Ren
a
,JunTang
b
,JunMa
a,∗
, Ying Xu
a
a
Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China
b
College of Science, China University of Mining and Technology, Xuzhou 221116, China
article info
Article history:
Received 3 March 2015
Revised 4 May 2015
Accepted 5 May 2015
Availableonline14May2015
Keywords:
Noise
Synchronization
Neuronal circuit
Single-chip microcomputer (SCM)
abstract
The Hindmarsh–Rose neuron mode can reproduce the main properties of neuronal activity,
and it is effective for dynamical investigation. Neuronal activity can also be verified by using
realistic circuits mapped from the theoretical neuronal models. The mode of electrical activity
of each neuron is dependent on the external forcing, connection coupling between neurons
and noise in the network or external uncertain driving. It is challenging to design reliable but
practical artificial neuronal circuits to study the transition of electrical activities of neurons.
In this paper, an artificial practical circuit is fabricated to reproduce the electrical activity of
neuron with different discharge modes, and detailed elements for this circuit are presented.
Additive noise is imposed on single neuronal circuit and the coupled neuronal circuits, and
then the noise-induced transition of electrical activity and the occurrence for synchronization
between neuronal circuits under optimized noise (moderate noise intensity) are investigated.
It is found that noise is helpful to activate quiescent neuronal circuit, and also possible to
induce synchronization between coupled neuronal circuits. And this practical neuronal circuit
is helpful for further study of collective behaviors of coupled neuronal network.
© 2015 Elsevier B.V. All rights reserved.
1. Introduction
Multiple modes of electrical activities of neurons in biological systems can be induced by appropriate external forcing, and
transition of discharge modes occurs due to the shift of bifurcation parameters [1–11]. Most of the theoretical neuronal models
are reliable for the study of mathematical neuroscience, for example, bifurcation analysis [12–15] is useful to understand the
transition of different electric modes [16] and synchronization problems [17–20], and some bifurcation discussion is consistent
with biological experimental results [21–23]. The realistic neuronal system often consists of a large number of neurons with
complex electrical activities, and complex network under different topologies is effective to discern the collective behaviors of
a large number of coupled neurons [24–27]. The electrical activities of neurons depend on the internal parameters, connection
action from other neurons and external forcing. Noise also plays an active role in regulating neuronal activities of neurons, for
example, stochastic and/or coherence resonance occurs under optimized noise, as a result, regularity or periodicity emerges
in the electrical activity of neuron, or neuronal network [28–34]. Based on these neuronal models, some realistic factors such
as time delay and noise are mapped into the neuronal model to detect the occurrence and transition of electrical activities in
neurons [35,36]. It is believed that small-world connection type for neurons is more reliable than a regular connection type to
describe the collective behaviors. In a realistic neuronal system, the probability of long range connection between neurons could
be time-varying instead of fixed connection probability [37], and thus the spatial pattern in the network can be generated with
∗
Corresponding author. Tel.: +86 15009310193.
E-mail address: hyperchaos@163.com, hyperchaos@lut.cn (J. Ma).
http://dx.doi.org/10.1016/j.cnsns.2015.05.001
1007-5704/© 2015 Elsevier B.V. All rights reserved.